This website uses cookies to deliver some of our products and services as well as for analytics and to provide you a more personalized experience. Click here to learn more. By continuing to use this site, you agree to our use of cookies. We've also updated our Privacy Notice. Click here to see what's new.

This website uses cookies to deliver some of our products and services as well as for analytics and to provide you a more personalized experience. Click here to learn more. By continuing to use this site, you agree to our use of cookies. We've also updated our Privacy Notice. Click here to see what's new.

About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

A detailed analysis of mode-locking is presented in which the nonlinear mode-coupling behavior in a waveguide array, dual-core fiber, and/or fiber array is used to achieve stable and robust passive mode-locking. By using the discrete, nearest-neighbor spatial coupling of these nonlinear mode-coupling devices, low-intensity light can be transferred to the neighboring waveguides and ejected (attenuated) from the laser cavity. In contrast, higher intensity light is self-focused in the launch waveguide and remains largely unaffected. This nonlinear effect, which is a discrete Kerr lens effect, leads to the temporal intensity discrimination required in the laser cavity for mode-locking. Numerical studies of this pulse shaping mechanism show that using current waveguide arrays, fiber-arrays, or dual-core fibers in conjunction with standard optical fiber technology, stable and robust mode-locked soliton-like pulses are produced.

Figures (13)

Fig. 1. Possible laser cavity configurations which include nonlinear mode-coupling (NLMC) as the mode-locking element. The fiber coupling to the NLMC is illustrated in Fig. 2. In addition to the basic setup, polarization controllers, isolators, and other stabilization mechanisms may be useful or required for successful operation.

Fig. 2. Schematic of butt-coupling implementation of NLMC element in the laser cavity configurations of Fig. 1. Three NLCM are depicted: (a) a waveguide array, (b) a dual-core fiber, and (c) a fiber array. In addition to the basic butt-coupling, index matching materials and tappering to account for core-size mismatch may be required to improve performance. Note that the figures are not drawn to scale.

Fig. 3. The classic representation of spatial diffraction and confinement of electromagnetic energy in a waveguide array considered by Peschel et al. [30]. In the top figure, the intensity is not strong enough to produce self-focusing and confinement in the center waveguide, whereas the bottom figure shows the self-focusing due to the NLMC. The effect of this spatial focusing on a temporal pulse is shown in Fig. 4. Note that light was launched in the center waveguide with initial amplitude A0(0) = 1 (top) and A0(0) = 3 (bottom)

Fig. 4. Temporal pulse shaping in the center waveguide via passage through the waveguide array in Fig. 3. The dotted lines show the input waveform (e.g. a hyperbolic secant pulse) while the solid lines show the output. For low intensities (a), the energy in the center waveguide diffracts to the neighboring waveguides as shown in Fig. 3(top). As the intensity is increased, the pulse is temporally compressed due to the resonant coupling of low intensity light to the other waveguides. The temporal reshaping is responsible for the mode-locking.

Fig. 5. Representation of the spatial diffraction and confinement of electromagnetic energy in a dual-core fiber. In the top figure, the intensity is not strong enough to produce self-focusing and confinement in the launch waveguide, whereas the bottom figure shows the self-focusing due to the NLMC. The effect of this spatial focusing on a temporal pulse is shown in Fig. 6. Note that light was launched in the the primary waveguide with initial amplitude A0(0) = 1 (top) and A0(0) = 3 (bottom)

Fig. 6. Temporal pulse shaping in the launch waveguide via passage through the dual-core fiber. The dotted lines show the input waveform (e.g. a hyperbolic secant pulse) while the solid lines show the output. For low intensities (a), the energy in the launch waveguide couples to the neighboring core as shown in Fig. 5(top). As the intensity is increased, the pulse is temporally compressed due to the resonant coupling of low intensity light to the neighboring core. The temporal reshaping is responsible for the mode-locking.

Fig. 7. Schematic of the fiber array configuration. Here the coupling is to the nearest neighbors. In a hexagonal configuration [41], the evanescent coupling is then dominated by six neighboring core modes.

Fig. 8. Intensity dependent spatial diffraction and confinement of electromagnetic energy in a fiber array. In the top figures (a), the intensity is not strong enough to produce self-focusing and confinement in the launch waveguide. Specifically, the electromagnetic field which is initially launched with A0,0 = 1 ((a)-left) quickly diffracts energy to its neighboring waveguides as it propagates over 2 cm ((a)-middle) and 4 cm ((a)-right). For sufficiently high intensities, A0,0 = 3, the self-focusing confines the energy to the launch waveguide over the propagation distances of 0, 2, and 4 cm ((b)-left, middle, and right respectively).

Fig. 9. Temporal pulse shaping in the launch waveguide via passage through a fiber array. The dotted lines show the input waveform (e.g. a hyperbolic secant pulse) while the solid lines show the output. For low intensities (a), the energy in the launch waveguide couples to the neighboring fiber cores as shown in Fig. 8(a). As the intensity is increased, the self-focusing begins to dominate and the pulse is temporally compressed due to the resonant coupling of low intensity light to the neighboring cores. The temporal reshaping is responsible for the mode-locking.

Fig. 10. Stable mode-locking using a waveguide array for (a) a fixed gain model g(Z) = g0 = 0.263 and (b) a saturable gain model of Eq. Eq. (2) with g0 = 0.7. The mode-locking is robust to the specific gain model, cavity parameter changes, and cavity perturbations. Here is is assumed that a 20% coupling loss occurs at the input and output of the waveguide array.

Fig. 11. Output temporal response of the waveguide array under stable mode-locked operation. The center panel depicts the input (dashed line) and output (solid line) in the center waveguide A0. The temporal output of the two nearest waveguides, A±1 and A±2, are also depicted. The central waveguide retains 94% of the incoming light while the neighboring waveguides contain 1.5% (A±1) and 2.7% (A±2). Note the characteristic shape of the temporal energy in the neighboring waveguides due to the nonlinear mode-coupling.

Fig. 12. Multi-pulse per round trip mode-locked operation for g(Z) = g0 = 0.475 and 40% loss before and after waveguide array. On average, there are 3–4 stabilized pulses in the cavity for the given gain.

Fig. 13. Stable mode-locking using (a) a dual-core fiber with g0 = 0.39 and (b) using a fiber array with g0 = 0.5. The mode-locking is robust to cavity parameter changes and cavity perturbations. Here is is assumed that a 20% coupling loss occurs at the input and output of the dual-core fiber and fiber array.